Answer: The correct option is (A) [tex]10+6i.[/tex]
Step-by-step explanation: We are given to select the correct notation for the following complex number :
[tex]z=\sqrt{-36}+10~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
[tex]\sqrt{-1}=i~~~~~\Rightarrow -1=i^2.[/tex]
Also, the standard notation of a complex number is given by
[tex]z=a+bi,[/tex] where a and b are real numbers.
From (i), we have
[tex]z\\\\=\sqrt{-36}+10\\\\=\sqrt{36\times(-1)}+10\\\\=\sqrt{36i^2}+10\\\\=6i+10\\\\=10+6i.[/tex]
Thus, the correct notation for the given complex number is [tex]10+6i.[/tex]
Option (A) is CORRECT.
